This book is the first of a two-volume basic introduction to enumerative combinatorics at a level suitable for graduate students and research mathematicians. Much of the book is devoted to the theory and application of generating functions, a fundamental tool in enumerative combinatorics.
The four chapters are devoted to an introduction to enumeration (suitable for advanced undergraduates), sieve methods (including the Principle of Inclusion-Exclusion), partially ordered sets, and rational generating functions. There are a large number of exercises, almost all provided with solutions. Which greatly augment the text and provide entry into many areas not covered directly in the text. The material was chosen to cover those parts of enumerative combinatorics of greatest applicability and with the most important connections with other areas of mathematics.
This revised edition contains new sections of updates and of supplementary problems.
Graduate students and research mathematicians who wish to apply combinatorics to their work will find this an authoritative reference.
Chapter 1 What Is Enumerative Combinatorics?
Chapter 2 Sieve Methods
Chapter 3 Partially Ordered Sets
Chapter 4 Rational Generating Functions